I would have to respectfully disagree: theoretically speaking the ones on the left have an intensified meaning, the causative meaning (make someone do) would be conveyed in להצחיק, to make laugh.

As to לצחק and it's biblical meaning: I broadly agree with Origumi, but at least in Gen 26:8 a sexual connotation seems to be implied, since the witnessing of Isaac מצחק with Rebecca is the decisive moment when Abimelech realizes they must be husband and wife. Therefore they must have been "fooling around" with each other in a way a brother and a sister wouldn't.

but at least in Gen 26:8 a sexual connotation seems to be implied, since the witnessing of Isaac מצחק with Rebecca is the decisive moment when Abimelech realizes they must be husband and wife. Therefore they must have been "fooling around" with each other in a way a brother and a sister wouldn't.